Quality-Related Locally Weighted Non-Gaussian Regression Based Soft Sensing for Multimode Processes

Modified Modeling Method of Quartz Crystal Resonator Frequency-Temperature Characteristic With Considering Thermal Hysteresis

The frequency-temperature ( f - T ) characteristic of quartz crystal resonators is an important topic closely related to the frequency-deviation compensation in the design of cost-effective oscillators. Traditional studies depict the f - T characteristic as a polynomial function (usually a cubic function). However, this omits the thermal hysteresis phenomenon and cannot provide a very accurate frequency compensation. To handle this issue, this article is to propose two modified f - T characteristic modeling methods with considering the thermal hysteresis. First, to reflect the thermal hysteresis property of quartz crystal resonators, a two-directional f - T model is designed by introducing two individual submodels for describing the increasing and decreasing temperature stages, respectively. Furthermore, to integrate the submodels and provide the more accurate frequency-deviation estimation, a holistic f - T characteristic model based on double-hidden layer extreme learning machine (DHL-ELM) is presented. Different from the basic ELM model, two hidden layers, including one deterministic nonlinear mapping and one random nonlinear activation layer, are constructed for a better description of f - T characteristic. To validate our studies, an experiment system is applied to obtain the testing data of the real crystal resonators, and the applications demonstrate the effectiveness of the proposed methods.

A Novel Just-in-Time Learning Strategy for Soft Sensing with Improved Similarity Measure Based on Mutual Information and PLS

In modern industrial process control, just-in-time learning (JITL)-based soft sensors have been widely applied. An accurate similarity measure is crucial in JITL-based soft sensor modeling since it is not only the basis for selecting the nearest neighbor samples but also determines sample weights. In recent years, JITL similarity measure methods have been greatly enriched, including methods based on Euclidean distance, weighted Euclidean distance, correlation, etc. However, due to the different influence of input variables on output, the complex nonlinear relationship between input and output, the collinearity between input variables, and other complex factors, the above similarity measure methods may become inaccurate. In this paper, a new similarity measure method is proposed by combining mutual information (MI) and partial least squares (PLS). A two-stage calculation framework, including a training stage and a prediction stage, was designed in this study to reduce the online computational burden. In the prediction stage, to establish the local model, an improved locally weighted PLS (LWPLS) with variables and samples double-weighted was adopted. The above operations constitute a novel JITL modeling strategy, which is named MI-PLS-LWPLS. By comparison with other related JITL methods, the effectiveness of the MI-PLS-LWPLS method was verified through case studies on both a synthetic Friedman dataset and a real industrial dataset.